Two rods are connected as shown. The rods are of the same length and same cross-sectional area. In the steady state,the temperature $(\theta)$ of the interface will be........ $^oC$

One end of a $2.35\,m$ long and $2.0\,cm$ radius aluminium rod $(K = 235\,W\cdot m^{-1}K^{-1})$ is held at $20^{\circ}C$. The other end of the rod is in contact with a block of ice at its melting point. The rate in $kg\cdot s^{-1}$ at which ice melts is (Take latent heat of fusion for ice as $\frac{10}{3} \times 10^5\,J\cdot kg^{-1}$)

$A$ cylindrical steel rod of length $0.10 \,m$ and thermal conductivity $50 \,Wm^{-1}K^{-1}$ is welded end to end to a copper rod of thermal conductivity $400 \,Wm^{-1}K^{-1}$ and of the same area of cross-section but $0.20 \,m$ long. The free end of the steel rod is maintained at $100^{\circ}C$ and that of the copper rod at $0^{\circ}C$. Assuming that the rods are perfectly insulated from the surroundings,the temperature at the junction of the two rods is ................... $^{\circ}C$.

Two materials having coefficients of thermal conductivity $3K$ and $K$ and thickness $d$ and $3d$,respectively,are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are $\theta_2$ and $\theta_1$ respectively $(\theta_2 > \theta_1)$. The temperature at the interface is

$A$ slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio $1 : 4$. If the free face of brass is at $100^\circ C$ and that of copper at $0^\circ C$,the temperature of the interface is ........ $^\circ C$.

The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_1$ and $T_2$ $(T_1 > T_2)$. The rate of heat transfer,$\frac{dQ}{dt}$,through the rod in a steady state is given by: